The final \(^7\) Li abundance in BBN is contributed both from the directly synthesized \(^7\) Li, as well as those from the \(^7\) Be EC decays and \(^7\) Be(\(n\) ,\(p\) )\(^7\) Li
reaction, however, the relic \(^7\) Li nuclei mainly come from the latter process because most of the directly synthesized \(^7\) Li is destroyed through the
\(^7\) Li(\(p\) ,\(\alpha \) )\(^4\) He reaction immediately. The \(^7\) Be production is determined by the balance between the reactions which synthesize it and those destruct
it. Therefore, it is essential to accurately determine thermonuclear rates for those reactions involving \(^7\) Be nuclide. The key synthesizing reaction for \(^7\) Be
is the \(^3\) He(\(\alpha \) ,\(\gamma \) )\(^7\) Be reaction, which has been studied very well by various experiments and theories [1]}, [2]}, [3]}, [4]}.
The reactions for destructing \(^7\) Be are \(^7\) Be(\(n\) ,\(p\) )\(^7\) Li and \(^7\) Be(\(n\) ,\(\alpha \) )\(^4\) He, of primary and secondary importance, respectively. For the
\(^7\) Be(\(n\) ,\(p\) )\(^7\) Li reaction, its cross section has been studied in detailed in a wide energy range from 0.025 eV up to 8 MeV [5]}, [6]}, which covers
entirely the BBN effective energy region. As for the \(^7\) Be(\(n\) ,\(\alpha \) )\(^4\) He reaction, it could play a non-negligible role in direct \(^7\) Be
destruction [7]}. However, up to now, the \(^7\) Be(\(n\) ,\(\alpha \) )\(^4\) He reaction rate adopted in the current BBN simulations and the reaction rate
library [8]} is still the very old Wagoner rate [9]}, which is a simple theoretical estimation involving only the direct-capture reaction
mechanism, and also without information on the sources of data and error estimate. In this work, we have derived the thermonuclear rate of
\(^7\) Be(\(n\) ,\(\alpha \) )\(^4\) He based on the available indirect experimental data of \(^4\) He(\(\alpha \) ,\(n\) )\(^7\) Be and \(^4\) He(\(\alpha \) ,\(p\) )\(^7\) Li reactions, with the
well-know charge symmetry and detailed-balance principle [10]}. With this new rate, we have examined its impact on the primordial \(^7\) Li abundance with
a BBN code.
